Investigations of the effects of back-barrier introduction on the two-dimensional electron gas (2DEG) of ultrathin-barrier AlN/GaN heterostructures with AlGaN and InGaN back-barriers are carried out using self-consistent solutions of 1-dimensional Schrodinger-Poisson equations. Inserted AlGaN and InGaN back-barriers are used to provide a good 2DEG confinement thanks to raising the conduction band edge of GaN buffer with respect to GaN channel layer. Therefore, in this paper the influence of these back-barrier layers on sheet carrier density, 2DEG confinement, and mobility are systematically and comparatively investigated. As a result of calculations, although sheet carrier density is found to decrease with InGaN back-barrier layer, it is not changed with AlGaN back-barrier layer for suggested optimise heterostructures. Obtained results can give some insights for further experimental studies.